Properties of equations of motion of interacting gauge fields of all spins in 3+1 dimensions

Properties of totally consistent equations of motion of interacting gauge fields of all spins s=0, 1/2, 1, . . ., infinity in 3+1 dimensions are discussed in some detail. The equations under consideration are explicitly general coordinate invariant, possess all necessary higher-spin gauge symmetries, reduce to the standard free massless equations in the linearized approximation and contain Einstein equations with the cosmological term in the spin-2 sector.